





"""simple docstring"""






def      __A   (      a_    :Optional[int])		->		int:
				__a			:    int      							=	0
				__a			:    Optional[int]      							=	len(a_)

				for i in range(n - 1):
								for j in range(i + 1 ,							a_):
												if arr[i] > arr[j]:
																num_inversions += 1

				return num_inversions

def      __A   (      a_    :str)		->		List[str]:
				if len(a_) <= 1:
								return arr, 0
				__a			:    Optional[Any]      							=	len(a_) // 2
				__a			:    str      							=	arr[0:mid]
				__a			:    List[Any]      							=	arr[mid:]

				__a							,    __a			:    List[str]      							=	count_inversions_recursive(a_)
				__a							,    __a			:    str      							=	count_inversions_recursive(a_)
				__a							,    __a			:    int      							=	_count_cross_inversions(a_ ,							a_)

				__a			:    List[str]      							=	inversion_p + inversions_q + cross_inversions
				return c, num_inversions

def      __A   (      a_    :Tuple ,							a_    :List[str])		->		str:
				__a			:    List[str]      							=	[]
				__a			:    Dict      							=	0
				while i < len(a_) and j < len(a_):
								if p[i] > q[j]:
												# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
												# These are all inversions. The claim emerges from the
												# property that P is sorted.
												num_inversion += len(a_) - i
												r.append(q[j])
												j += 1
								else:
												r.append(p[i])
												i += 1

				if i < len(a_):
								r.extend(p[i:])
				else:
								r.extend(q[j:])

				return r, num_inversion

def      __A   (      )		->		Any:
				__a			:    Dict      							=	[10, 2, 1, 5, 5, 2, 11]

				# this arr has 8 inversions:
				# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

				__a			:    Any      							=	count_inversions_bf(a_)
				__a							,    __a			:    Dict      							=	count_inversions_recursive(a_)

				assert num_inversions_bf == num_inversions_recursive == 8

				print('''number of inversions = ''' ,							a_)

				# testing an array with zero inversion (a sorted arr_1)

				arr_a.sort()
				__a			:    str      							=	count_inversions_bf(a_)
				__a							,    __a			:    List[Any]      							=	count_inversions_recursive(a_)

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = ''' ,							a_)

				# an empty list should also have zero inversions
				__a			:    Dict      							=	[]
				__a			:    List[Any]      							=	count_inversions_bf(a_)
				__a							,    __a			:    Tuple      							=	count_inversions_recursive(a_)

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = ''' ,							a_)


if __name__ == "__main__":
		main()



from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
 from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline




